Question

1.Ten thousand student of dire dawa university are normally distributed with the mean,µ of 60 inches and the standard deviation of 3 inches.

A. what is the probability that the height of any one student chosen at random is between 60 and 65 inches?

B. if a random sample of 50 student is taken,what is the probability that the mean height of this sample will be between 50 and 70 inches

Answer 1

1) $P(60<X<65)=P(\frac{60-60}{3}<X<\frac{65-60}{3})=P(0<Z<1.67)=$

$=P(Z<1.67)-P(Z<0)=0.9525-0.5=0.4525.$

2) $P(50<\bar X<70)=P(\frac{50-60}{\frac{3}{\sqrt{50}}}<Z<\frac{70-60}{\frac{3}{\sqrt{50}}})=P(-23.57<Z<23.57)=$

$=P(Z<23.57)-P(Z<-23.57)=1-0=1.$